Testing Additive Separability of Error Term in Nonparametric Structural Models
提出一种检验非参数结构模型中误差项是否可加的方法，利用控制变量使回归变量与误差独立，基于偏导数为1的观察构造统计量，并通过蒙特卡洛模拟验证其有限样本性能。
This article considers testing additive error structure in nonparametric structural models, against the alternative hypothesis that the random error term enters the nonparametric model nonadditively. We propose a test statistic under a set of identification conditions considered by Hoderlein et al. (2012 Hoderlein , S. , Su , L. , White , H. ( 2012 ). Specification testing for nonparametric structural models with monotonicity in unobservables. Discussion Paper, Dept. of Economics, University of California San Diego . [Google Scholar]), which require the existence of a control variable such that the regressor is independent of the error term given the control variable. The test statistic is motivated from the observation that, under the additive error structure, the partial derivative of the nonparametric structural function with respect to the error term is one under identification. The asymptotic distribution of the test is established, and a bootstrap version is proposed to enhance its finite sample performance. Monte Carlo simulations show that the test has proper size and reasonable power in finite samples.